Maxwell-Voigt and Voigt Models for Vibration Isolation: Influence of Fractional Damping and Time Delay

2018 ◽  
Author(s):  
Sudhir Kaul
Keyword(s):  
Time Delay ◽  
Frequency Response ◽  
Fractional Order ◽  
Vibration Isolation ◽  
Damping Ratio ◽  
Maximum Amplitude ◽  
Damping Force ◽  
Fractional Damping ◽  
Integer Order ◽  
Voigt Model

This paper presents results from a follow-up study of fractional damping and time delay. Fractional damping has been used in the literature to demonstrate certain advantages over integer-order damping in many applications involving viscoelastic characteristics. It is observed that fractional damping can be used to influence stability boundaries, natural frequencies and vibration amplitudes, thus providing modeling flexibility in predicting the response of an isolated system during preliminary design. Additionally, time delay or lag is known to be inherent in a damped system, therefore a direct representation of time delay in modeling the damping force is expected to enhance model fidelity. This paper investigates the use of Voigt and Maxwell-Voigt models that incorporate fractional damping and time delay. In this paper, fractional damping has been particularly introduced to investigate possible improvements in the frequency response. Results indicate that fractional damping can be used to significantly enhance the capability of the Voigt model. The influence of the fractional order is found to be analogous to the damping ratio in an integer-order model. Fractional order is seen to exhibit a somewhat limited influence on the Maxwell-Voigt model. However, attributes such as the peak frequency and maximum amplitude are seen to be directly influenced by the fractional order. Although time delay is seen to exhibit an influence on the frequency response, it needs to be limited within useful bounds. Overall, it is observed that fractional order and time delay can be used to improve the accuracy of the Voigt and Maxwell-Voigt models. These enhanced models can be used for the design and development of elastomeric isolators and vibration isolation systems.

Influence of Fractional Damping and Time Delay on Maxwell-Voigt Model for Vibration Isolation

2016 ◽  
Author(s):  
Sudhir Kaul
Keyword(s):  
Time Delay ◽  
Dynamic Characteristics ◽  
Vibration Isolation ◽  
Model Parameters ◽  
Fractional Damping ◽  
Vibration Isolators ◽  
Multiple Parameters ◽  
Realistic Representation ◽  
Voigt Model ◽  
Isolation Systems

Models of vibration isolators are very commonly used for the design and analysis of isolation systems. Accurate isolator modeling is critical for a successful prediction of the dynamic characteristics of isolated systems. Isolators exhibit a complex behavior that depends on multiple parameters such as frequency, displacement amplitude, temperature and loading conditions. Therefore, it is important to choose a model that is accurate while adequately representing the relationships with relevant parameters. Recent literature has indicated some inherent advantages of fractional derivatives that can be exploited in the modeling of elastomeric isolators. Furthermore, time delay of damping is also seen to provide a realistic representation of damping. This paper examines the Maxwell-Voigt model with fractional damping and a time delay. This model is compared with the conventional Maxwell-Voigt model (without time delay or fractional damping) and the Voigt model in order to comprehend the influence of fractional damping and time delay on dynamic characteristics. Multiple simulations are performed after identifying model parameters from the data collected for a passive elastomeric isolator. The analysis results are compared and it is observed that the Voigt model is highly sensitive to fractional damping as well as time delay.

scholarly journals The Effect of Fractional Damping and Time-delayed Feedback on the Stochastic Resonance of Asymmetric SD Oscillator

2021 ◽  
Author(s):  
Qiubao Wang ◽  
Hao Wu ◽  
Yuejuan Yang
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Vibration Isolation ◽  
Weak Signal Detection ◽  
Fractional Damping ◽  
System Parameters ◽  
Sd Oscillator ◽  
Delay Feedback Control ◽  
Detection Energy ◽  
Time Delayed Feedback

Abstract This paper proposes the stiffness nonlinearities and asymmetric SD (smooth and discontinuous) oscillators under time-delay feedback control with a fractional damping. With the effect of displacement and velocity feedback, the oscillator is adjusted to the desired vibration state and then the stochastic resonance (SR) is achieved. This article discusses the contribution of various system parameters and time-delay feedback to SR, especially which induced by fractional damping. It should be noted that this paper provides effective guidance for fault diagnosis and weak signal detection, energy harvesting, vibration isolation and vibration reduction.

Dynamic Analysis and Parameter Identification of a Single Mass Elastomeric Isolation System Using a Maxwell-Voigt Model

2006 ◽  
Vol 128 (6) ◽  
pp. 713-721 ◽  
Author(s):  
Jie Zhang ◽  
Christopher M. Richards
Keyword(s):  
Parameter Identification ◽  
Dynamic Analysis ◽  
Frequency Response ◽  
Natural Frequency ◽  
Damping Ratio ◽  
Response Spectra ◽  
Isolation System ◽  
Single Mass ◽  
Voigt Model ◽  
Stiffness And Damping

Dynamic analysis and parameter identification of a single mass elastomeric isolation system represented by a Maxwell-Voigt model is examined. Influences that the stiffness and damping values of the Maxwell element have on natural frequency, damping ratio, and frequency response are uncovered and three unique categories of Maxwell-type elements are defined. It is also shown that Voigt and Maxwell-Voigt models with equivalent natural frequencies and damping ratios can have considerably different frequency response spectra. Lastly, a parameter identification method is developed for identifying Maxwell-Voigt models from frequency response spectra. The method is based on constant natural frequency and damping ratio curves generated from modal analysis of potential Maxwell-Voigt models.

scholarly journals Frequency Response Based Curve Fitting Approximation of Fractional–Order PID Controllers

2019 ◽  
Vol 29 (2) ◽  
pp. 311-326 ◽  
Author(s):  
Kishore Bingi ◽  
Rosdiazli Ibrahim ◽  
Mohd Noh Karsiti ◽  
Sabo Miya Hassam ◽  
Vivekananda Rajah Harindran
Keyword(s):  
Frequency Response ◽  
Frequency Domain ◽  
Fractional Order ◽  
Curve Fitting ◽  
Order Approximation ◽  
Frequency Range ◽  
Approximation Techniques ◽  
Integer Order ◽  
The Best Approximation ◽  
Fractional Order Pid

Abstract Fractional-order PID (FOPID) controllers have been used extensively in many control applications to achieve robust control performance. To implement these controllers, curve fitting approximation techniques are widely employed to obtain integer-order approximation of FOPID. The most popular and widely used approximation techniques include the Oustaloup, Matsuda and Cheraff approaches. However, these methods are unable to achieve the best approximation due to the limitation in the desired frequency range. Thus, this paper proposes a simple curve fitting based integer-order approximation method for a fractional-order integrator/differentiator using frequency response. The advantage of this technique is that it is simple and can fit the entire desired frequency range. Simulation results in the frequency domain show that the proposed approach produces better parameter approximation for the desired frequency range compared with the Oustaloup, refined Oustaloup and Matsuda techniques. Furthermore, time domain and stability analyses also validate the frequency domain results.

scholarly journals Study on a Class of Piecewise Nonlinear Systems with Fractional Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Meiqi Wang ◽  
Wenli Ma ◽  
Enli Chen ◽  
Yujian Chang
Keyword(s):  
Time Delay ◽  
Nonlinear System ◽  
Frequency Response ◽  
Dynamic Model ◽  
Fractional Order ◽  
Excitation Frequency ◽  
Order Parameters ◽  
Response Characteristics ◽  
Amplitude Frequency Response ◽  
Frequency Response Characteristics

In this paper, a dynamic model of piecewise nonlinear system with fractional-order time delay is simplified. The amplitude frequency response equation of the dynamic model of piecewise nonlinear system with fractional-order time delay under periodic excitation is obtained by using the average method. It is found that the amplitude of the system changes when the external excitation frequency changes. At the same time, the amplitude frequency response characteristics of the system under different time delay parameters, different fractional-order parameters, and coefficient are studied. By analyzing the amplitude frequency response characteristics, the influence of time delay and fractional-order parameters on the stability of the system is analyzed in this paper, and the bifurcation equations of the system are studied by using the theory of continuity. The transition sets under different piecewise states and the constrained bifurcation behaviors under the corresponding unfolding parameters are obtained. The variation of the bifurcation topology of the system with the change of system parameters is given.

scholarly journals Robust Stability of Fractional Order Time-Delay Control Systems: A Graphical Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Radek Matušů ◽  
Roman Prokop
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Fractional Order ◽  
Robust Stability ◽  
Irrigation Canal ◽  
Graphical Approach ◽  
Delay Term ◽  
Integer Order ◽  
Robust Stability Analysis ◽  
Value Sets

The paper deals with a graphical approach to investigation of robust stability for a feedback control loop with an uncertain fractional order time-delay plant and integer order or fractional order controller. Robust stability analysis is based on plotting the value sets for a suitable range of frequencies and subsequent verification of the zero exclusion condition fulfillment. The computational examples present the typical shapes of the value sets of a family of closed-loop characteristic quasipolynomials for a fractional order plant with uncertain gain, time constant, or time-delay term, respectively, and also for combined cases. Moreover, the practically oriented example focused on robust stability analysis of main irrigation canal pool controlled by either classical integer order PID or fractional order PI controller is included as well.

scholarly journals Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

2021 ◽  
Author(s):  
Ehsan Kharazmi ◽  
Min Cai ◽  
Xiaoning Zheng ◽  
Guang Lin ◽  
George Em Karniadakis
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Fractional Order ◽  
Control Measures ◽  
Time Dependent ◽  
Multiple Time ◽  
Epidemiological Models ◽  
Integer Order ◽  
Delay Models ◽  
Fractional Differential

ABSTRACTWe analyze a plurality of epidemiological models through the lens of physics-informed neural networks (PINNs) that enable us to identify multiple time-dependent parameters and to discover new data-driven fractional differential operators. In particular, we consider several variations of the classical susceptible-infectious-removed (SIR) model by introducing more compartments and delay in the dynamics described by integer-order, fractional-order, and time-delay models. We report the results for the spread of COVID-19 in New York City, Rhode Island and Michigan states, and Italy, by simultaneously inferring the unknown parameters and the unobserved dynamics. For integer-order and time-delay models, we fit the available data by identifying time-dependent parameters, which are represented by neural networks (NNs). In contrast, for fractional differential models, we fit the data by determining different time-dependent derivative orders for each compartment, which we represent by NNs. We investigate the identifiability of these unknown functions for different datasets, and quantify the uncertainty associated with NNs and with control measures in forecasting the pandemic.

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